A simple proof of the fundamental theorem of Galois theory
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866915903573065728 |
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| author | Brandenburg, Martin |
| author_facet | Brandenburg, Martin |
| contents | We present a simple proof of the fundamental theorem of Galois theory, which establishes a correspondence between the intermediate fields of a finite Galois extension and the subgroups of its Galois group. The proof is based on the combinatorial fact that a field cannot be expressed as the union of finitely many proper subfields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_07508 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A simple proof of the fundamental theorem of Galois theory Brandenburg, Martin Number Theory History and Overview 12-02, 12F05, 12F10 We present a simple proof of the fundamental theorem of Galois theory, which establishes a correspondence between the intermediate fields of a finite Galois extension and the subgroups of its Galois group. The proof is based on the combinatorial fact that a field cannot be expressed as the union of finitely many proper subfields. |
| title | A simple proof of the fundamental theorem of Galois theory |
| topic | Number Theory History and Overview 12-02, 12F05, 12F10 |
| url | https://arxiv.org/abs/2211.07508 |